Tail index regression studies how covariates affect tail heaviness in heavy-tailed data. In many applications, data are distributed across heterogeneous sources, where direct pooling is infeasible due to privacy or regulatory constraints. Existing methods mainly focus on single-dataset analysis and do not address heterogeneous federated settings. We develop a personalized federated framework for high-dimensional tail index regression that accommodates client heterogeneity while exploiting latent similarities across clients. The proposed estimator combines sparsity regularization with nonconcave fusion penalties to perform coefficient estimation, variable selection, and group recovery. We establish non-asymptotic convergence rates and show that the estimator enjoys an oracle property by consistently recovering the underlying grouping structure. For computation, we develop an ADMM-based federated algorithm with adaptive gradient updates and establish its convergence guarantees. We further propose a debiased federated inference procedure based on adaptive weighted aggregation across related clients, yielding valid confidence intervals and hypothesis tests with improved efficiency over target-only inference. Simulation studies and real-data analysis demonstrate the effectiveness of the proposed methods.

翻译：尾指数回归研究协变量如何影响重尾数据中尾部的重程度。在许多应用中，数据分布于异质来源，由于隐私或监管约束，直接合并数据不可行。现有方法主要侧重于单数据集分析，无法解决异质联邦场景。我们针对高维尾指数回归开发了个性化联邦框架，该框架在利用客户端间潜在相似性的同时，适应客户端异质性。所提出的估计量结合稀疏正则化与非凹融合惩罚，用于系数估计、变量选择和组别恢复。我们建立了非渐近收敛速率，并证明该估计量通过一致恢复底层分组结构而具有oracle性质。在计算方面，我们开发了基于ADMM的联邦算法，其中包含自适应梯度更新，并建立了其收敛保证。我们进一步提出基于相关客户端间自适应加权聚合的去偏联邦推断流程，从而生成有效的置信区间和假设检验，其效率优于仅针对目标客户端的推断。仿真实验和真实数据分析验证了所提方法的有效性。